I would like to define my own isomorphism of two graphs. I want to check if two graphs are isomorphic given that each edge has some attribute --- basically the order of placing each edge. I wonder if one can use the method:
networkx.is_isomorphic(G1,G2, edge_match=some_callable)
somehow by defining function some_callable()
.
For example, the following graphs are isomorphic, because you can relabel the nodes to obtain one from another.
Namely, relabel [2<->3].
But, the following graphs are not isomorphic.
There is no way to obtain one from another by re-labeling the nodes.
Here you go. This is exactly what the edge_match
option is for doing. I'll create 3 graphs the first two are isomorphic (even though the weights have different names --- I've set the comparison function to account for that). The third is not isomorphic.
import networkx as nx
G1 = nx.Graph()
G1.add_weighted_edges_from([(0,1,0), (0,2,1), (0,3,2)], weight = 'aardvark')
G2 = nx.Graph()
G2.add_weighted_edges_from([(0,1,0), (0,2,2), (0,3,1)], weight = 'baboon')
G3 = nx.Graph()
G3.add_weighted_edges_from([(0,1,0), (0,2,2), (0,3,2)], weight = 'baboon')
def comparison(D1, D2):
#for an edge u,v in first graph and x,y in second graph
#this tests if the attribute 'aardvark' of edge u,v is the
#same as the attribute 'baboon' of edge x,y.
return D1['aardvark'] == D2['baboon']
nx.is_isomorphic(G1, G2, edge_match = comparison)
> True
nx.is_isomorphic(G1, G3, edge_match = comparison)
> False